If it wasn't "inferior", then why did the modern style take over? You
could argue that it was linked to something else that provided a
significant advantage, but in the absence of any such explanation it seems
simplest to assume that the modern style is "superior" (i.e.,
confers significant reproductive advantage).

I take your point. However, I think it's a case of apples and oranges.
_Archaeopteryx_'s style of flight was (presumably) very different to that of
modern birds. I don't know why or how it flew, and we'll probably never
know for sure. However, there are probably many reasons why the modern
avian body plan "took over" - associated with the ability to fly long
distances, to better maneuver in flight, to catch prey on the wing, etc.
But _Archaeopteryx_ may not have needed any of these things. Its style of
flight was suitable for its limited purposes. Each to his own, I guess is
what I'm saying.

The other reason why I avoid terms like "inferior" and "superior" when
discussing evolution is that it implies progress. I know what you're
getting at when you use these terms; but they do have baggage. In terms of
numbers of species, passerine birds outnumber all other kinds of birds
combined; but I wouldn't say that passerines are "superior" to ratites or
penguins or birds of prey.

(Of course, Archie's style must have been "superior" to that of its
predecessors.)

Again, this is apples and oranges (or oranges and pomegranates). Anyway,
Archie's style may not even be "superior" to its predecessors. For example,
the microraptorans may exemplify one of the pre-_Archaeoptyeryx_ stages in
the evolution of flight. Although microraptoran taxonomy may currently be
oversplit, microraptoran species are rather common in the Jehol biota.
There may have been microraptoran-style gliders everwhere in the Early
Cretaceous, and they may have outnumbered _Archaeopteryx_-style fliers.